IMAC 27 - Orlando, FL Shaker Excitation

Size: px

Start display at page:

Download "IMAC 27 - Orlando, FL Shaker Excitation"

Paulina Washington
6 years ago
Views:

IMAC 27 - Orlando, FL - 2009 Peter Avitabile UMASS

1 IMAC 27 - Orlando, FL Peter Avitabile UMASS Lowell Marco Peres The Modal Shop 1 Dr. Peter Avitabile

2 Objectives of this lecture: Overview some shaker excitation techniques commonly employed in modal testing Review deterministic and non-deterministic methods Present excitation techniques that have developed from a historical standpoint Present some MIMO testing information 2 Dr. Peter Avitabile

Vibration Shaker Qualification vs Modal Shaker Many people are familiar with vibration shakers used for qualification of equipment where specific loading is applied to replicate the actual operating

3 Vibration Shaker Qualification vs Modal Shaker Many people are familiar with vibration shakers used for qualification of equipment where specific loading is applied to replicate the actual operating environment. F I X T U R E ATTACHMENT FIXTURE EXPANDER HEAD SHAKER MOUNTING TABLE SHAKER ARMATURE TEST ITEM DRIVER COIL SHAKER BODY SHAKER BASE This is a much different testing technique than what is done for modal testing (where high loads are not applied to the structure) 3 Dr. Peter Avitabile

for Modal Testing Excitation device is attached to the structure using a long rod called a stinger or quill STRUCTURE UNDER TEST STINGER RESPONSE TRANSDUCER FORCE TRANSDUCER SHAKER Its purpose is to

4 for Modal Testing Excitation device is attached to the structure using a long rod called a stinger or quill STRUCTURE UNDER TEST STINGER RESPONSE TRANSDUCER FORCE TRANSDUCER SHAKER Its purpose is to provide input along the shaker excitation axis with essentially no excitation of the other directions It is also intended to be flexible enough to not provide any stiffness to the other directions The force gage is always mounted on the structure side of the quill NOT ON THE SHAKER SIDE 4 Dr. Peter Avitabile

5 Excitation Configuration Shaker Test Signal -random -burst Random -pseudo-random -periodic-random -Chirp Stinger force sensor AUTORANGING structure AVERAGING Power Amplifier AUTORANGING AVERAGING WITH WINDOW AUTORANGING AVERAGING Dr. Peter Avitabile

Reason for Stinger Purpose of Stinger Decouple shaker from test structure Force transducer between stinger and structure decouple forces acting in the axial direction only

6 Reason for Stinger Purpose of Stinger Decouple shaker from test structure Force transducer between stinger and structure decouple forces acting in the axial direction only Forces acting in any other direction will be unaccounted for creating error in the measurements Modal Shaker Axial Bending Force Gage Stinger Structure 6 Dr. Peter Avitabile

7 Possible Problems with Stinger Suspect increase in stiffness when stinger is at higher location Axial stiffness Axial and bending stiffness 7 Dr. Peter Avitabile

8 Stinger Configuration with Through Hole Shaker 2-part chuck assembly Force sensor Modal Exciter collet Test Structure armature stinger 8 Dr. Peter Avitabile

9 Common Stingers Piano wire Modal stinger Threaded metal rod Threaded nylon rod 9 Dr. Peter Avitabile

10 Common Stingers Types of Stingers Available Drill Rod Threaded Rod Metal Nylon Piano Wire Axial stiffness provided through a preload on wire Essentially no lateral stiffness Requires shaker and test fixture to be fixed 10 Dr. Peter Avitabile

11 CORRECT Force gage divorces the stinger/ shaker from the structure WRONG Stinger becomes part of the test structure 11 Dr. Peter Avitabile

12 The Overall Measurement Process INPUT OUTPUT INPUT FORCE OUTPUT RESPONSE WINDOWED SIGNAL WINDOWED INPUT WINDOWED OUTPUT AVERAGED INPUT, OUTPUT AND CROSS SPECTRA AVERAGED INPUT POWER SPECTRUM AVERAGED CROSS POWER SPECTRUM AVERAGED OUTPUT POWER SPECTRUM COMPUTED FREQUENCY RESPONSE FUNCTION AND COHERENCE FREQUENCY RESPONSE FUNCTION COHERENCE FUNCTION 12 Dr. Peter Avitabile

13 Signal Types Excitation techniques can be broken down into two categories: Deterministic Signals Non-Deterministic (Random) Signals 13 Dr. Peter Avitabile

14 Signal Types - Deterministic Deterministic Signals conform to a particular mathematical relationship can be described exactly at any instant in time response of the system can also be exactly defined if the system character is known swept sine, sine chirp, digital stepped sine are examples 14 Dr. Peter Avitabile

15 Signal Types Non-Deterministic Non-Deterministic (Random) Signals do not conform to a particular mathematical relationship can not be described exactly at any instant in time described by some statistical character of the signal generally have varying amplitude, phase and frequency content at any point in time pure random, periodic random, burst random are examples 15 Dr. Peter Avitabile

16 Signal Types Deterministic vs Non-Deterministic Good for IDENTIFICATION of system linearity Deterministic Signals conform to a particular mathematical relationship can be described exactly at any instant in time response of the system can also be exactly defined if the system character is known examples :swept sine, sine chirp, digital stepped sine Good for LINEARIZATION of slight nonlinearities Non-Deterministic (Random) Signals do not conform to a particular mathematical relationship can not be described exactly at any instant in time described by some statistical character of the signal generally have varying amplitude, phase and frequency content at any point in time examples: pure random, periodic random, burst random 16 Dr. Peter Avitabile

17 Excitation Signal Characteristics RMS to Peak Signal to Noise Distortion Test Time Controlled Frequency Content Controlled Amplitude Content Removes Distortion Content Characterizes Non Linearites 17 Dr. Peter Avitabile

18 Summary Excitation Signal Characteristics Ref: University of Cincinnati 18 Dr. Peter Avitabile

19 Remarks on General Excitation Characteristics The complete solution of a forced harmonic 2 F x 2 x x 0 && + ζωn & + ωn = excitation will result in m two parts of the response transient part which decays with time and - the steady state part of the response sin ωt x(t) = F k 0 + X e 1 1 ζω n t ω ω sin sin( ωt φ) n ζ ( ) 2 1 ζ ω t + φ n ω ω n 1 2 Steady State Transient 19 Dr. Peter Avitabile

20 Remarks on General Excitation Characteristics The complete solution of a forced harmonic excitation will result in two parts of the response transient part which decays with time and - the steady state part of the response F x 2 x x 0 && + ζωn & + ωn = sin ωt m x(t) = F k 0 + X e 1 1 ζω n t ω ω sin sin( ωt φ) n ζ ( ) 2 1 ζ ω t + φ n ω ω n 1 2 Steady State Transient 20 Dr. Peter Avitabile

21 Vibrations Convolution for SDOF Sine Excitation Start of Sine Steady State Reached End of Transient Sine input AVI 21 Dr. Peter Avitabile

22 Swept Sine Excitation INPUT EXCITATION OUTPUT TIME RESPONSE Slowly changing sine signal sweeping from one frequency to another frequency 22 Dr. Peter Avitabile

Analog Slow Swept Sine Excitation A slowly changing sine output sweeping from one frequency to another frequency ADVANTAGES best peak to RMS level best signal to noise ratio good for

23 Analog Slow Swept Sine Excitation A slowly changing sine output sweeping from one frequency to another frequency ADVANTAGES best peak to RMS level best signal to noise ratio good for nonlinear characterization widely accepted and understood DISADVANTAGES slowest of all test methods leakage is a problem does not take advantage of speed of FFT process 23 Dr. Peter Avitabile

24 Random Excitation AUTORANGING AVERAGING An ergodic, stationary signal with Gaussian probability distribution. Typically, has frequency content at all frequencies. 24 Dr. Peter Avitabile

25 Random Excitation An ergodic, stationary signal with Gaussian probability distribution. Typically, has frequency content at all frequencies. ADVANTAGES gives a good linear approximation for a system with slight nonlinearities relatively fast relatively good general purpose excitation DISADVANTAGES leakage is a very serious problem FRFs are generally distorted due to leakage 25 Dr. Peter Avitabile

26 Random Excitation Time signal Frequency Signal 1 OUTPUT INPUT 0s 1.999s 0Hz 400Hz COHERENCE FRF 0s 1.999s 0Hz AVG: Hz Notice that the coherence is very poor at all frequencies 26 Dr. Peter Avitabile

27 Random Excitation Effects of averaging -40 CH1 Pwr Spec db Mag CH1 Pwr Spec db Mag 0Hz AVG: 1 800Hz CH1 Pwr Spec db Mag 0Hz AVG: Hz Hz AVG: Hz 27 Dr. Peter Avitabile

28 Random Excitation with Hanning Window AUTORANGING AVERAGING WITH WINDOW An ergodic, stationary signal with Gaussian probability distribution. Typically, has frequency content at all frequencies. 28 Dr. Peter Avitabile

29 Random Excitation with Hanning Window An ergodic, stationary signal with Gaussian probability distribution Typically, has frequency content at all frequencies. ADVANTAGES gives a good linear approximation for a system with slight non linearities relatively fast overlap processing can be used relatively good general purpose excitation DISADVANTAGES even with windows applied to the measurement leakage is a very serious problem FRFs are generally distorted due to leakage with (significant distortion at the peaks) excessive averaging necessary to reduce variance on data 29 Dr. Peter Avitabile

30 Random Excitation with Hanning Window Time signal Frequency Signal OUTPUT INPUT 0s 1.999s 0Hz 400Hz COHERENCE FRF 0s 1.999s 0Hz AVG: Hz Notice that the coherence is very poor at resonant frequencies 30 Dr. Peter Avitabile

31 Random Excitation with Overlap Processing OVERLAP PROCESSING used to reduce test time with pure random excitations Hanning window tends to weight the first and last quarter of the time block to zero and this data is not effectively used in the normal averaging process effectively uses the portion of the block that has been heavily weighted to zero overlap processing allows for almost twice as many averages with the same data when fifty percent overlap is used 31 Dr. Peter Avitabile

32 Pseudo Random Excitation AUTORANGING AVERAGING IFT An ergodic, stationary signal consisting of only integer multiples of the FFT frequency increment. Signal has constant amplitude with varying phase. Note that the transient part of the signal must decay and steady state response achieved before measurements are taken to assure leakage free FRF. 32 Dr. Peter Avitabile

33 Pseudo Random Excitation An ergodic, stationary signal consisting of only integer multiples of the FFT frequency increment. Signal has constant amplitude with varying phase. ADVANTAGES always periodic in the sample interval relatively fast fewer averages than random frequency spectrum is shapeable DISADVANTAGES sensitive to nonlinearities same excitation is used for each average 33 Dr. Peter Avitabile

34 Periodic Random Excitation AUTORANGING AVERAGE AUTORANGING AVERAGE IFT IFT 1 2 An ergodic, stationary signal consisting of only integer multiples of the FFT frequency increment. Signal has varying amplitude with varying phase. Note that the transient part of the signal must decay and steady state response achieved before measurements are taken to assure leakage free FRF. 34 Dr. Peter Avitabile

35 Periodic Random Excitation An ergodic, stationary signal consisting of only integer multiples of the FFT frequency increment. Signal has varying amplitude with varying phase. ADVANTAGES always periodic in the sample interval frequency spectrum is shapable determines a very good linear approximation of the FRF since leakage is minimized DISADVANTAGES a different signal is generated for each measurement longest of all excitation techniques except swept sine 35 Dr. Peter Avitabile

36 Burst Random Excitation AUTORANGING AVERAGING Current ~ force Voltage ~ velocity A random excitation that exists over only a portion of the data block (typically 50% to 70%). NOTE: Voltage mode amplifier necessary creates back emf effect to dampen response at end of burst 36 Dr. Peter Avitabile

37 Burst Random Excitation A random excitation that exists over only a portion of the data block (typically 50% to 70%) ADVANTAGES has all the advantages of random excitation the function is self-windowing no leakage DISADVANTAGES if response does not die out within on sample interval, then leakage is a problem 37 Dr. Peter Avitabile

38 Burst Random Excitation Time signal Frequency Signal End of burst OUTPUT INPUT Shaker off 0s 1.999s Response decays exponentially 0Hz 400Hz COHERENCE FRF 0s 1.999s 0Hz AVG: Hz Notice that the coherence is very good even at resonant frequencies Notice the sharpness of the resonances and measurement quality. 38 Dr. Peter Avitabile

39 Sine Chirp Excitation AUTORANGING AVERAGING A very fast swept sine signal that starts and stops within one sample interval of the FFT analyzer 39 Dr. Peter Avitabile

40 Sine Chirp Excitation A very fast swept sine signal that starts and stops within one sample interval of the FFT analyzer ADVANTAGES has all the same advantages as swept sine self windowing function good for nonlinear characterization DISADVANTAGES nonlinearities will not be averaged out 40 Dr. Peter Avitabile

41 Sine Chirp Excitation Time signal Frequency Signal OUTPUT INPUT 0s 1.999s 0Hz 400Hz COHERENCE FRF 0s 1.999s 0Hz AVG: Hz Notice that the coherence is very good. Notice the sharpness of the resonances and measurement quality. 41 Dr. Peter Avitabile

42 Digital Stepped Sine Excitation AUTORANGING AVERAGE AUTORANGING AVERAGE IFT IFT Sine waves are generated at discrete frequencies which correspond to the digital values of the FFT analyzer for the frequency resolution available. The system is excited with a single sine wave and steady state response measured. Once one spectral line is obtained, the next digital frequency is acquired until all frequencies have been measured. 42 Dr. Peter Avitabile

43 Digital Stepped Sine Excitation Sine waves are generated at discrete frequencies which correspond to the digital values of the FFT analyzer for the frequency resolution available. The system is excited with a single sine wave and the steady state response is measured. Once one spectral line is obtained, the next digital frequency is acquired until all frequencies have been measured. ADVANTAGES excellent peak to RMS level excellent signal to noise ratio good for nonlinear characterization leakage free measurements obtained DISADVANTAGES slowest of all test methods 43 Dr. Peter Avitabile

44 Comparison - Random/Hann, Burst Random, Chirp RANDOM BURST RANDOM SINE CHIRP 44 Dr. Peter Avitabile

45 Random with Hanning Window vs Burst Random Frequency Response Function Coherence RANDOM RANDOM BURST RANDOM BURST RANDOM When comparing the measurement with random and burst random, notice that the random excitation peaks are lower and appear to be more heavily damped when compared to the burst random. - also notice the coherence improvement at the resonant peaks. 45 Dr. Peter Avitabile

46 Random with Hanning Window vs Burst Random RANDOM COH FRF BURST RANDOM RANDOM & HANNING BURST RANDOM 46 Dr. Peter Avitabile

47 Random with Hanning Window vs Burst Random COH FRF RANDOM & HANNING BURST RANDOM 47 Dr. Peter Avitabile

48 Random with Hanning Window vs Burst Random BURST RANDOM RANDOM 117Hz 143Hz Windows will always have an effect on the measured FRF even when the same window is applied to both input and output signals There will always be a distortion at the peak and the appearance of higher damping Windows always, always, always,... distort data!!! 48 Dr. Peter Avitabile

49 Linearity Check with Sine Chirp Excitation ONE FORCE UNIT FIVE FORCE UNITS TEN FORCE UNITS 49 Dr. Peter Avitabile

50 Shaped Spectrum S H A P E D S P E C T R U M E X C I T A T I O N Uncontrolled broadband excitation techniques are used for most modal testing performed today. However, the relatively flat excitation spectrum causes a wide variation in the response accelerometers. This may be a problem when tesing sensitive equipment. A shaped spectrum, that is contolled, provides an input level that complements the response of the system. This provides a better usage of the ADC since wide variations in level over the frequency range of interest are minimized. 50 Dr. Peter Avitabile

51 Shaped Spectrum 51 Dr. Peter Avitabile

52 Multiple Input Multiple Output Shaker Testing 52 Dr. Peter Avitabile

53 Multiple Input Objectives of this lecture: Discuss several practical aspects of multiple input multiple output shaker testing Discuss some tools commonly used in MIMO testing 53 Dr. Peter Avitabile

Multiple columns of FRF matrix acquired More consistent

54 Multiple Input Provide a more even distribution of energy Simultaneously excite all modes of interest Multiple columns of FRF matrix acquired More consistent data is collected Same test time as SISO case 54 Dr. Peter Avitabile

55 Excitation Considerations - MIMO Multiple referenced FRFs are obtained from MIMO test Energy is distributed better throughout the structure making better measurements possible Ref#1 Ref#2 Ref#3 55 Dr. Peter Avitabile

56 Multiple Input Multiple Output Shaker Testing [ G XF] = [ H][ G FF ] [ H] H H = M H No,1 H H H M No,2 L L L H H H 1,Ni 2,Ni M No,Ni Measurements are developed in a similar fashion to the single input single output case but using a matrix formulation [ H ] = [ ][ ] 1 G XF G FF where No - number of outputs Ni - number of inputs 56 Dr. Peter Avitabile

57 MIMO Testing - Principal Component Analysis Check for independent shaker inputs. Perform a SVD on the input shaker matrix commonly called Principal Component Analysis [ G ] = [ U][ S][ V] T FF The singular values of the SVD should produce large singular values at all frequencies for all shaker excitations. This indicates that the shaker excitation are linearly independent and inversion is possible 57 Dr. Peter Avitabile

58 Multiple and Partial Coherence Two additional coherence functions are needed: Multiple coherence defines how much of the output signal is linearly related to all of the measured input signals. It is very similar to the ordinary coherence of the single input case. Partial coherence relates how much of the measured output signal is linearly related to one of the measured input signal with the effects of the other measured input signals removed. All of the partial coherences sum together to form the multiple coherence. 58 Dr. Peter Avitabile

59 Principal Component Analysis Check for shaker linear independence 59 Dr. Peter Avitabile

60 MIMO FRF and Multiple Coherence Typical MIMO measurements acquired 60 Dr. Peter Avitabile

61 SISO vs MIMO FRF SISO FRF MIMO FRF 61 Dr. Peter Avitabile

62 Blue Frame -SISO vs MIMO -Reciprocity Checks RANDOM WITH WINDOW SINGLE INPUT SINGLE OUTPUT TESTING BURST RANDOM RANDOM WITH WINDOW BURST RANDOM MULTIPLE INPUT MULTIPLE OUTPUT TESTING 62 Dr. Peter Avitabile

63 Blue Frame -SISO vs MIMO -Reciprocity Checks FRFs look reasonably similar SISO - RANDOM - HANNING - REF #1 & #2 MIMO - RANDOM - HANNING - REF #1 & #2 but take a closer look SISO - BURST RANDOM - REF #1 & #2 MIMO - BURST RANDOM - REF #1 & #2 63 Dr. Peter Avitabile

64 Blue Frame -SISO vs MIMO -Reciprocity Checks S I S O SISO - RANDOM - HANNING - REF #1 SISO - RANDOM - HANNING - REF #1 & #2 Notice the variance on the FRF measured and the peak shifting SISO - RANDOM - HANNING - REF #2 RANDOM HANNING 64 Dr. Peter Avitabile

65 Blue Frame -SISO vs MIMO -Reciprocity Checks SISO - BURST RANDOM - REF #1 SISO - BURST RANDOM - REF #2 S I S O SISO - BURST RANDOM - REF #1 & #2 BURST RANDOM Burst random improves the data but the peaks of the FRFs do not remain the same when single shaker testing is performed 65 Dr. Peter Avitabile

66 Blue Frame -SISO vs MIMO -Reciprocity Checks MIMO - RANDOM - HANNING - REF #1 MIMO - RANDOM - HANNING - REF #2 M I M MIMO - RANDOM - HANNING - REF #1 & #2 RANDOM HANNING O MIMO random improves the consistency but there are other differences that can be seen at the antiresonance 66 Dr. Peter Avitabile

67 Blue Frame -SISO vs MIMO -Reciprocity Checks M I M O MIMO - BURST RANDOM - REF #1 MIMO - BURST RANDOM - REF #1 & #2 MIMO burst random improves the data in all respects MIMO - BURST RANDOM - REF #2 BURST RANDOM 67 Dr. Peter Avitabile

68 Blue Frame -SISO vs MIMO -Reciprocity Checks SISO/MIMO - BURST RANDOM - REF #1 & #2 SISO/MIMO - BURST RANDOM - REF #1 & #2 The peaks are definitely shifted relative to the SISO and MIMO data But which is the actual mode??? 68 Dr. Peter Avitabile

69 Excitation Considerations - MIMO Large or complicated structures require special attention 69 Dr. Peter Avitabile

70 Excitation Considerations - MIMO Multiple shakers are needed in order to adequately shaker the structure with sufficient energy to be able to make good measurements for FRF estimation 70 Dr. Peter Avitabile

71 Excitation Considerations - MIMO Flimsy dryer cabinet MIMO test 71 Dr. Peter Avitabile

72 Excitation Considerations - MIMO Complicated structures require special attention when measuring frequency response functions for modal testing. Extremely lightweight structures are very difficult to test and obtain high quality FRFs 72 Dr. Peter Avitabile

73 Excitation Considerations - MIMO Measurements on the same structure can show tremendously different modal densities depending on the location of the measurement 73 Dr. Peter Avitabile

74 Things no one ever told me!!! Shaker testing is very powerful but there are many issues that must be understood. Some of these are identified on the next pages 74 Dr. Peter Avitabile

500 Here is an example of a stinger flexibility due to rotation effects the

75 Reciprocity Even on simple structures, reciprocity can be a problem but not due to the structure 0 (m/s2)/n db FRF 6:-X / 2:+X FRF 2:-X / 6:+X Hz 500 Here is an example of a stinger flexibility due to rotation effects the upper portion of the structure has a rotational effect 75 Dr. Peter Avitabile

Reciprocity SISO FRF Measurements Using SISO, several measurements were made at different locations as shown 20 g/n db FRF 1:-Z/3:-Z FRF 3:-Z/1:-Z -100 0 Hz 900

76 Reciprocity SISO FRF Measurements Using SISO, several measurements were made at different locations as shown 20 g/n db FRF 1:-Z/3:-Z FRF 3:-Z/1:-Z Hz 900 While only a few sample measurements are shown, there is an effect of the shaker location on the structure and the rotational stinger effect. 76 Dr. Peter Avitabile

77 Stinger Alignment or Damaged Stinger An incorrectly aligned stinger or a poorly fabricated stinger can ruin a test (g/lbf db ) 40 Stinger Alignment Effects Damaged Stinger Effect g/lbf db (m/s2)/n db ((m/s2)/n) db ( Straight Stinger Bent Straight Stinger Bent Stinger Impact Hz Straight Stinger Straight Stinger Poorly Fabricated Damaged Stinger Stinger Hz Here are two examples of the effect on an FRF measurement due to these problems 77 Dr. Peter Avitabile

78 Stinger Length The length of the stinger can also have an impact on the measured response (g/lbf db ) Stinger Length Comparisons Stinger Length Comparisons 1 inch 3 inch 5 inch 7 inch Impact (g/lbf) db 1 inch 3 inch 5 inch 7 inch Impact Hz Hz Too short a stinger will have higher lateral stiffness and too long a stinger will have flexibility Dr. Peter Avitabile

79 Stinger Type There are many different stinger types Stinger Type Comparison 20 (g/lbf) db g/lbf db Thin Drill Rod Thick Drill Rod Piano Wire Thin Drill Rod Thick Drill Rod Piano Wire Nylon Threaded Rod Steel Threaded Rod Impact Nylon Threaded Rod Steel Threaded Rod Impact Hz Hz 900 Thin Drill Rod Thick Drill Rod Piano Wire Nylon Threaded Rod Steel Threaded Rod Impact Hz 625 There can be an effect due to these differences 79 Dr. Peter Avitabile

80 IMAC 27 - Orlando, FL Peter Avitabile UMASS Lowell Marco Peres The Modal Shop 80 Dr. Peter Avitabile

Excitation Techniques Do s and Don ts

Peter Avitabile UMASS Lowell Excitation Techniques Do s and Don ts Marco Peres The Modal Shop 1 Dr. Peter Avitabile Excitation Considerations Objectives of this lecture: Overview impact testing considerations